Home > matpower6.0 > cpf_corrector.m

cpf_corrector

PURPOSE ^

CPF_CORRECTOR Solves the corrector step of a continuation power flow

SYNOPSIS ^

function [V, converged, i, lam] = cpf_corrector(Ybus, Sbusb, V_hat, ref, pv, pq,lam_hat, Sbust, Vprv, lamprv, z, step, parameterization, mpopt)

DESCRIPTION ^

CPF_CORRECTOR  Solves the corrector step of a continuation power flow
   [V, CONVERGED, I, LAM] = CPF_CORRECTOR(YBUS, SBUSB, V_HAT, REF, PV, PQ, ...
                                       LAM_HAT, SBUST, VPRV, LPRV, Z, ...
                                       STEP, PARAMETERIZATION, MPOPT)

   Computes the corrector step of a continuation power flow using a
   full Newton method with selected parameterization scheme.

   Inputs:
       YBUS : complex bus admittance matrix
       SBUSB : handle of function returning nb x 1 vector of complex
               base case injections in p.u. and derivatives w.r.t. |V|
       V_HAT :  predicted complex bus voltage vector
       REF : vector of indices for REF buses
       PV : vector of indices of PV buses
       PQ : vector of indices of PQ buses
       LAM_HAT : predicted scalar lambda
       SBUST : handle of function returning nb x 1 vector of complex
               target case injections in p.u. and derivatives w.r.t. |V|
       VPRV : complex bus voltage vector at previous solution
       LAMPRV : scalar lambda value at previous solution
       STEP : continuation step length
       Z : normalized tangent prediction vector
       STEP : continuation step size
       PARAMETERIZATION : Value of cpf.parameterization option.
       MPOPT : Options struct

   Outputs:
       V : complex bus voltage solution vector
       CONVERGED : Newton iteration count
       I : Newton iteration count
       LAM : lambda continuation parameter

   See also RUNCPF.

CROSS-REFERENCE INFORMATION ^

This function calls: This function is called by:

SOURCE CODE ^

0001 function [V, converged, i, lam] = cpf_corrector(Ybus, Sbusb, V_hat, ref, pv, pq, ...
0002                 lam_hat, Sbust, Vprv, lamprv, z, step, parameterization, mpopt)
0003 %CPF_CORRECTOR  Solves the corrector step of a continuation power flow
0004 %   [V, CONVERGED, I, LAM] = CPF_CORRECTOR(YBUS, SBUSB, V_HAT, REF, PV, PQ, ...
0005 %                                       LAM_HAT, SBUST, VPRV, LPRV, Z, ...
0006 %                                       STEP, PARAMETERIZATION, MPOPT)
0007 %
0008 %   Computes the corrector step of a continuation power flow using a
0009 %   full Newton method with selected parameterization scheme.
0010 %
0011 %   Inputs:
0012 %       YBUS : complex bus admittance matrix
0013 %       SBUSB : handle of function returning nb x 1 vector of complex
0014 %               base case injections in p.u. and derivatives w.r.t. |V|
0015 %       V_HAT :  predicted complex bus voltage vector
0016 %       REF : vector of indices for REF buses
0017 %       PV : vector of indices of PV buses
0018 %       PQ : vector of indices of PQ buses
0019 %       LAM_HAT : predicted scalar lambda
0020 %       SBUST : handle of function returning nb x 1 vector of complex
0021 %               target case injections in p.u. and derivatives w.r.t. |V|
0022 %       VPRV : complex bus voltage vector at previous solution
0023 %       LAMPRV : scalar lambda value at previous solution
0024 %       STEP : continuation step length
0025 %       Z : normalized tangent prediction vector
0026 %       STEP : continuation step size
0027 %       PARAMETERIZATION : Value of cpf.parameterization option.
0028 %       MPOPT : Options struct
0029 %
0030 %   Outputs:
0031 %       V : complex bus voltage solution vector
0032 %       CONVERGED : Newton iteration count
0033 %       I : Newton iteration count
0034 %       LAM : lambda continuation parameter
0035 %
0036 %   See also RUNCPF.
0037 
0038 %   MATPOWER
0039 %   Copyright (c) 1996-2016, Power Systems Engineering Research Center (PSERC)
0040 %   by Ray Zimmerman, PSERC Cornell,
0041 %   Shrirang Abhyankar, Argonne National Laboratory,
0042 %   and Alexander Flueck, IIT
0043 %
0044 %   Modified by Alexander J. Flueck, Illinois Institute of Technology
0045 %   2001.02.22 - corrector.m (ver 1.0) based on newtonpf.m (MATPOWER 2.0)
0046 %
0047 %   Modified by Shrirang Abhyankar, Argonne National Laboratory
0048 %   (Updated to be compatible with MATPOWER version 4.1)
0049 %
0050 %   This file is part of MATPOWER.
0051 %   Covered by the 3-clause BSD License (see LICENSE file for details).
0052 %   See http://www.pserc.cornell.edu/matpower/ for more info.
0053 
0054 %% default arguments
0055 if nargin < 14
0056     mpopt = mpoption;
0057 end
0058 
0059 %% options
0060 tol     = mpopt.pf.tol;
0061 max_it  = mpopt.pf.nr.max_it;
0062 
0063 %% initialize
0064 converged = 0;
0065 i = 0;
0066 V = V_hat;          %% initialize V with predicted V
0067 Va = angle(V);
0068 Vm = abs(V);
0069 lam = lam_hat;      %% initialize lam with predicted lam
0070 
0071 %% set up indexing for updating V
0072 npv = length(pv);
0073 npq = length(pq);
0074 nb = length(V);         %% number of buses
0075 j1 = 1;         j2 = npv;           %% j1:j2 - V angle of pv buses
0076 j3 = j2 + 1;    j4 = j2 + npq;      %% j3:j4 - V angle of pq buses
0077 j5 = j4 + 1;    j6 = j4 + npq;      %% j5:j6 - V mag of pq buses
0078 j7 = j6 + 1;    j8 = j6 + 1;        %% j7:j8 - lambda
0079 
0080 %% evaluate F(x0, lam_hat), including transfer/loading
0081 Sb = Sbusb(Vm);
0082 St = Sbust(Vm);
0083 mis = V .* conj(Ybus * V) - Sb - lam * (St - Sb);
0084 F = [   real(mis([pv; pq]));
0085         imag(mis(pq))   ];
0086 
0087 %% evaluate P(x0, lambda0)
0088 P = cpf_p(parameterization, step, z, V, lam, Vprv, lamprv, pv, pq);
0089 
0090 %% augment F(x,lambda) with P(x,lambda)
0091 F = [ F; 
0092       P ];
0093 
0094 %% check tolerance
0095 normF = norm(F, inf);
0096 if mpopt.verbose > 1
0097     fprintf('\n it    max P & Q mismatch (p.u.)');
0098     fprintf('\n----  ---------------------------');
0099     fprintf('\n%3d        %10.3e', i, normF);
0100 end
0101 if normF < tol
0102     converged = 1;
0103     if mpopt.verbose > 1
0104         fprintf('\nConverged!\n');
0105     end
0106 end
0107 
0108 %% do Newton iterations
0109 while (~converged && i < max_it)
0110     %% update iteration counter
0111     i = i + 1;
0112     
0113     %% evaluate Jacobian
0114     [dSbus_dVm, dSbus_dVa] = dSbus_dV(Ybus, V);
0115     [dummy, neg_dSdb_dVm] = Sbusb(Vm);
0116     [dummy, neg_dSdt_dVm] = Sbust(Vm);
0117     dSbus_dVm = dSbus_dVm - neg_dSdb_dVm - lam * (neg_dSdt_dVm - neg_dSdb_dVm);
0118     
0119     j11 = real(dSbus_dVa([pv; pq], [pv; pq]));
0120     j12 = real(dSbus_dVm([pv; pq], pq));
0121     j21 = imag(dSbus_dVa(pq, [pv; pq]));
0122     j22 = imag(dSbus_dVm(pq, pq));
0123     
0124     J = [   j11 j12;
0125             j21 j22;    ];
0126 
0127     Sxf = St - Sb;
0128     dF_dlam = -[real(Sxf([pv; pq])); imag(Sxf(pq))];
0129     [dP_dV, dP_dlam] = cpf_p_jac(parameterization, z, V, lam, Vprv, lamprv, pv, pq);
0130 
0131     %% augment J with real/imag -Sxfr and z^T
0132     J = [   J   dF_dlam; 
0133           dP_dV dP_dlam ];
0134 
0135     %% compute update step
0136     dx = -(J \ F);
0137 
0138     %% update voltage
0139     if npv
0140         Va(pv) = Va(pv) + dx(j1:j2);
0141     end
0142     if npq
0143         Va(pq) = Va(pq) + dx(j3:j4);
0144         Vm(pq) = Vm(pq) + dx(j5:j6);
0145     end
0146     V = Vm .* exp(1j * Va);
0147     Vm = abs(V);            %% update Vm and Va again in case
0148     Va = angle(V);          %% we wrapped around with a negative Vm
0149 
0150     %% update lambda
0151     lam = lam + dx(j7:j8);
0152 
0153     %% evalute F(x, lam)
0154     Sb = Sbusb(Vm);
0155     St = Sbust(Vm);
0156     mis = V .* conj(Ybus * V) - Sb - lam * (St - Sb);
0157     F = [   real(mis(pv));
0158             real(mis(pq));
0159             imag(mis(pq))   ];
0160 
0161     %% evaluate P(x, lambda)
0162     P = cpf_p(parameterization, step, z, V, lam, Vprv, lamprv, pv, pq);
0163 
0164     %% augment F(x,lambda) with P(x,lambda)
0165     F = [ F; 
0166           P ];
0167 
0168     %% check for convergence
0169     normF = norm(F, inf);
0170     if mpopt.verbose > 1
0171         fprintf('\n%3d        %10.3e', i, normF);
0172     end
0173     if normF < tol
0174         converged = 1;
0175         if mpopt.verbose
0176             fprintf('\nNewton''s method corrector converged in %d iterations.\n', i);
0177         end
0178     end
0179 end
0180 
0181 if mpopt.verbose
0182     if ~converged
0183         fprintf('\nNewton''s method corrector did not converge in %d iterations.\n', i);
0184     end
0185 end

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